DEM modelling of the dynamic penetration process onMars as a part of the NASA InSight Mission

J. Poganski*1,2, H. F. Schweiger2 , G. Kargl1 and N. I. Kömle1

1 Space Research Institute, Graz, Austria2 Institute of Soil Mechanics and Foundation Engineering, Graz, Austria

* Corresponding Author

ABSTRACT The NASA InSight Mission will be launched in March 2016 and will land on the surface of Mars about nine months later.The InSight Mission provides new knowledge on the early evolution of planets in our solar system. Therefor it is necessary to investigatethe deep interior of Mars. One instrument on board of the lander is the HP³ Mole which penetrates itself five meters deep into the surface ofMars to measure the planetary heat flow. The mechanical response of the soil during the penetration provides an unique opportunity toderive an accurate mechanical characterisation of the Martian soil. Numerical simulations will be used to predict the Mole performance andthe maximum reachable depth in advance. Furthermore, the numerical model of the soil will be used to reconstruct the behaviour of theMartian soil afterwards. The discrete element method was chosen to simulate the high dynamics and the large displacements of the soil thatoccurs from the dynamic penetration process of the HP³ Mole. This paper contains simulation of a standard CPT with constant penetrationrate using different boundary assumptions and a dynamic CPT with a single stroke.

1 INTRODUCTION

The investigation of planets in our solar system pro-vides knowledge about processes that have alreadybeen taken on earth millions of years ago. That iswhy the NASA InSight Mission provides new knowl-edge on the evolution and history of our planet. As a part of this Mission the HP³ Mole which is gen-erally used for the heat flow measurements in deepinterior of Mars, gives the opportunity to derive amechanical characterisation of Martian soil. So farthere exist just rough assumptions about the mechani-cal behaviour of Martian soil due to the imprints ofthe wheels of the Mars Exploration Rovers and byanalysing the stability of natural slopes [1], [2]. The HP³ Mole drives itself with a hammering mecha-nism into the surface of Mars. The mechanical re-sponse of the soil is obtained by measuring the posi-tion and the resistance force of the Mole during pene-tration. The exact position and inclination of the

Mole is measured by the extended length of the sci-ence tether, which connects the Mole with the sup-porting structure at the surface (Figure 1), and an em-bedded inclinometer.

Figure 1. The HP³ Mole and the supporting structure.

At the landing site of the InSight-lander the soil isexpected to be cohesionless dry sand with a smallamount of blocky material. The investigation of the

science tetherMole

supporting structure

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landing region is done with several images of the sur-face of Mars (Figure 2). The surface is analysed forrocks, slopes and craters, and also a long-term obser-vation is done to estimate the surface winds at thelanding region.

Figure 2. Digital elevation model of 1 meter slopes.

The mechanical behaviour as response of the penetra-tion process is very complex and requires numericalsupport. Therefor, an extended finite element methodand a discrete element method were compared andevaluated considering the challenges of solving thisproblem involving high dynamics and large deforma-tions.

2 NUMERICAL SIMULATION

For preliminary numerical simulations, a comparisonof a discrete element method based code and a finiteelement method based code has been performed. Thefollowing software was investigated:

LIGGGHTS (DEM) by DCS-Computing Material Point Method (MPM) by Deltares

The benchmark of a quasi-static cone penetration testwas used for comparison. The computations takenearly the same time, whereas coarse-graining isused in the DEM and mass scaling is used in theMPM. The numerical technique of coarse-graining means ascale up of the particle size using a fixed scale. Allinteraction models in the DEM are independent of

the particle radius, which allows to scale the particlesize without changing the particle behaviour. The in-crease of the inertia mass is balanced by the smalleramount of particles that are used for the same region.The technique of mass scaling means an increase ofthe density combined with a decrease of the gravityby the same scale. Thus, it is possible to increase thetime step, which speeds up the simulation. The disad-vantage of the mass scaling technique is that it is notapplicable for dynamical simulations. In this case, theinertia mass would be incorrect and so the accelera-tion forces would not be correctly calculated. The discrete element method is chosen for the simu-lation of the penetration process, because of its bettercapability performing dynamic simulations as re-quired in this problem.

2.1 Calibration of materials

The calibration of material behaviour is an importantand elaborate part of the discrete element method.Since the soil behaviour in the DEM is mainly de-fined by the rearrangement of particles, it becomesmore difficult to generate a certain behaviour by ad-justing the particle scale parameters. Also it is notpossible to investigate the mechanics of a singlegrain to derive the particle scale parameters, becauseit must be noticed that the grain properties can be dif-ferent from the particle properties. This is caused byeffects due to the real grain shape which are tried tobe captured by appropriate particle parameters. Onlythe bulk behaviour of the particles shall represent thebulk behaviour of the soil. Therefore, the calibrationof materials is done by comparing the soil responseof macro-scale laboratory experiments with numeri-cal models. The experiments used for the calibrationare:

Angle of repose experiment Oedometer test Triaxial compression test Inclined plane

It is important to use at least one test with a highstress state like the oedometer test, because the re-structuring under high pressure is highly dependent

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on small rotations and movements of particles. Usingthe elastic-plastic spring-dashpot rolling model fromJ. Ai [5] gives accurate results under low stress states,but for high stress states, i.e. for unloading andreloading under high compression, the rolling modelleads to undesirable behaviour. This is caused by thesaving of the deformation energy in the spring part ofthe rolling model, which is more or less recovered indeformation at unloading. Therefore, the rollingmodel is changed to capture the soil behaviour at un-loading and reloading more accurately.

2.2 Quasi-static cone penetration

The numerical simulation of a quasi-static cone pene-tration is investigated to obtain information about theinfluence of the boundaries and the particle sizes.The plot of the particle velocities (Figure 3) illus-trates the differences between fixed walls near thepenetrator and damped moving walls that hold a cer-tain confining pressure. Due to the fixed walls theparticles at the sides of the penetrator need to be up-lifted in order to have space for the penetrator,whereas with the absorbent moving walls the parti-cles can be pushed to the sides. The uplift of the par-ticles causes a higher resistance force on the penetra-tor.

Figure 3. Velocity plot of a quasi-static cone penetration using fixed boundaries (left side) and absorbent boundaries (right side).

The difference of the resistance force between fixedboundaries and absorbent boundaries increases withdepth, because of the larger amount of particles thatneed to be uplifted (Figure 4).

Figure 4. Resistance force on penetrator over depth.

The difference in penetration resistance betweenspecimens with fixed boundaries and stress con-trolled boundaries with a constant confining pressurehas already been investigated by Butlanska et al. [3].

0 0,05 0,1 0,15 0,2

0

10

20

30

40

50

60

f ixed boundary

absorbent boundary

Depth [m]

Re

sis

tan

ce

fo

rce

[N

]

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2.3 Dynamic cone penetration

The numerical simulation of a dynamic cone penetra-tion takes higher numerical effort than the quasi-static penetration. Due to the dynamic strokes of thepenetrator locally high accelerations of particles oc-cur, which will result in a pressure wave propagationthrough the soil. The reflection of these pressurewaves at the boundaries influences the resistanceforce and thereby the displacement of the penetratorper stroke. The absorbent boundaries are used toavoid these reflections. The dynamic cone penetration tests in the laboratoryof DLR were always done in a container with stiffwalls. Hence, it is necessary to add an elastic springpart to the absorbent boundaries in order to take intoaccount the reflections at the walls. The force profilerepresenting the stroke of the internal hammer mech-anism of the mole forcing the penetrator is approxi-mated as half of a sine curve with a certain time in-terval and magnitude, which has been taken from cal-culations of a one dimensional pile drive model [4]. The simulation of the dynamic penetration is done ina small chamber with spring-dashpot boundaries atthe sides and the bottom, and a top plate with a de-fined mass to simulate different overburden pres-sures.

Figure 5. Simulation of a dynamic cone penetration.

The wave propagation of the acceleration forces startspherical from the tip of the penetrator (Figure 5).Also some particle at the shaft are accelerated by thefriction between penetrator and soil, but this is a

small part compared to the particles pushed by thetip. The aim of these simulations is to estimate a reach-able depth of the HP³ Mole in advance and also togenerate a validated numerical soil sample of Martiansoil by back-calculations of the measurements fromthe HP³ Mole.

3 SUMMARY AND CONCLUSIONS

The progress data from the penetration of the HP³Mole in the Martian soil provide a uniqueopportunity to derive an accurate mechanicalcharacterization of the Martian soil at the landingsite. The simulation of the initial penetration processwill provide a first prediction of the maximumreachable depth and gives a better understanding ofthe mechanical soil behaviour on Mars by back-calculations afterwards. A discrete element method ischosen for the simulation of the penetration process.The DEM is able to simulate high dynamics withinthe soil and allows insights into the particle scaleinteractions. The gained knowledge about theMartian soil behaviour can be used for the planningof future missions on Mars and of course it is animportant information to understand how the planetwas formed.

ACKNOWLEDGEMENT

The first author wishes to acknowledge the fundingof this work by the FFG grant 844356.

REFERENCES

[1] Perko, H., Nelson, J., and Green, J. (2006). ”Mars Soil Me-chanical Properties and Suitability of Mars Soil Simulants.” J.Aerosp. Eng., 19(3), 169-176.[2] Zöhrer, A. (2006). “Laboratory Experiments and NumericalkModelling of Cone Penetration Tests into various Martian Soil

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Analogue Materials”, Ph.D., Graz University of Technology, Aus-tria.[3] Butlanska, J., Arroyo, M., Gens, A., and O'Sullivan, C. (2014).“Multi-scale analysis of cone penetration test (CPT) in a virtualcalibration chamber”, Can. Geotech. J., 51(1), 51-66. [4] Kömle, N. I., Poganski, J., Kargl, G. and Grygorczuk, J.(2015). “Pile driving models for the evaluation of soil penetrationresistance measurements from planetary subsurface probes”, Plan-etary and Space Science, Volumes 109-110, May 2015, Pages 135-148.[5] Ai, J., Chen, J., Rotter, J.M., and Ooi, J.Y. (2011). “Assessmentof rolling resistance models in discrete element simulations”, Pow-der Technology, 206, 269-282.

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